
Following Gasper and Rahman [1]}, the basic hypergeometric series \(_{r+1}\phi _r\)  is defined by
\(\begin{split}_{r+1}\phi _{r}\left[\begin{array}{c}a_1,a_2,\ldots ,a_{r+1}\\b_1,b_2,\ldots ,b_{r}\end{array};q,\, z\right]=\sum _{k=0}^{\infty }\frac{(a_1,a_2,\ldots , a_{r+1};q)_k}{(q,b_1,\ldots ,b_{r};q)_k} z^k.\end{split}\) 
